3. Except that it doesn't

The 'helix' is very inaccurate.

Look carefully at his animation of heliocentric motion. He shows the direction of the Sun's motion around the galaxy as the same as the plane of the planets' orbits. But this is not the case. The solar system's plane is tipped with respect to the galaxy by about a 60° angle, like the way a car's windshield makes an angle with respect to the car's forward motion.

This is actually critical: In the helical model, he shows the planets as orbiting around the Sun perpendicular to the motion of the Sun around the galaxy; "face-on", if you like. This is wrong. Because the orbits of the planets are tipped by 60°, not 90°, they can sometimes be ahead and sometimes behind the Sun. That right there, and all by itself, shows this helical depiction is incorrect. In the real model, heliocentrism, you do get that sort of ahead-and-behind motion, exactly as we observe in the real sky.